Method and machine for generating cam surfaces



F. B. BURT Nov. 1, 1960 METHOD AND MACHINE FOR GENERATING CAM SURFACES 4 Sheets-Sheet 1 Filed Jan. 23, 1957 INVENTOR. P 'ARLow B. Bun-r B ATTORNEY Nov. 1, 1960 F. B. BURT 2,958,264

METHOD AND MACHINE FOR GENERATING CAM SURFACES Filed Jan. 23, 1957 4 Sheets-Sheet 2 INVENTOR.

FARLow B. BURT BY 3 ATTOR EIY NOV. 1, 1960 BURT 2,958,264

METHOD AND MACHINE. FOR GENERATING CAM SURFACES Filed Jan. 23, 1957 4 Sheets-Sheet 3 INVENTOR.

FARLOW B. BURT BY ATTOZNEY Nov. 1, 1960 F. B. BURT 2,958,264

METHOD AND momma FOR GENERATING CAM SURFACES Filed Jan. 25, 1957 4 Sheets-Sheet 4 IN VENTOR.

P I fif- A FARLOW B. BURT ATT RNEY United fitates Patent 1 2,958,264 METHOD AND MACHINE FOR GENERATING CAM SURFACES Farlow B. Burt, South Bend, Ind, assignor to The Bendix Corporation, a corporation of Delaware Filed Jan. 23, 1957, Ser. No. 635,747 6 Claims. (Cl. 90-15) The present invention relates to method and apparatus for accurately forming cam surfaces of the type having continuously repeating sections spaced about an axis of rotation; and to a particular shape of cam surface which can be accurately produced very economically by further refinements in this method.

An object of the present invention is the provision of new and improved apparatus for forming cam surfaces of the above described type.

A more particular object of the present invention is the provision of new and improved apparatus in which a rotating cutting element is maintained tangent to the desired cam contour when forming cam surfaces of the above mentioned type.

A more specific object of the invention is the provision of a new and improved method and apparatus for causing a rotating cutting element to be maintained tangent to the desired cam contour when forming surfaces of the above mentioned type in which a rotatable means is provided which, when synchronously driven in predetermined phase relationship to the angular position of the cutting element relative to the blank, causes the center of the cutting element to be spaced radially from the desired cam contour by the radius of the cutting ele ment, and in which the rotatable means is alternately speeded up and slowed down to vary the phase relationship between the cutting element and blank according to a predetermined cycle which maintains the periphery of the cutting clement tangent to the desired cam contour.

A further object of the invention is the provision of new and improved cam forming apparatus having first means for providing relative rotation between a blank and the center of a rotatable cutting element, second means for reciprocating the blank and cutting element radially with respect to each other in timed relation to the first means, and third means for speeding up and slowing down at least one of said first and second means according to a predetermined cycle to maintain the periphery of said rotatable cutting element tangent to the desired cam contour.

Another object of the invention is the provision of new and improved apparatus of the immediately above described type for generating a cam contour formed from a continuously repeating sinusoidal configuration, in which apparatus said third means comprises a pair of cylindrically shaped gears rotated about respective points located a predetermined distance from their geometric centers.

Another object of the invention is the provision of a new and improved cam configuration having a plurality of lobes and valleys positioned radially about an axis of rotation with the tips of the lobes being uniformly machined to provide cylindrical surfaces of fixed radius from the axis of rotation-the lobes and valleys being preferably formed by a continuously repeating sinusoidal configuration, and the cylindrical surfaces preferably having a length of from two to five degrees.

Another object of the invention is the provision of a new and improved method of generating the preferred cam surface mentioned above by means of the apparatus also mentioned above in which the rotatable cutting element is positioned radially with" respect to the blank while the center of the cutting element and blank are rotated relative to each other to provide a cylindrical 2,958,264 Patented Nov. 1, 1960 'ice surface of fixed radius, and thereafter the sinusoidal valleys are formed by relative radial reciprocating movement between the cutting element and blank until the remaining sections of the cylindrical surface are machined to a predetermined length.

Further objects and advantages will become apparent to those skilled in the art to which the invention relates from the following description of the preferred embodiments described with reference to the accompanying drawings forming a part of this specification, in which:

Figure 1 is a perspective view of apparatus embodying principles of the present invention;

Figure 2 is a cross-sectional view taken on the line 2-2 of Figure 1;

Figure 3 is a side view of a cam member finish machined according to the preferred cam configuration;

Figure 4 is a fragmentary side view of a portion of Figure 3 better illustrating a refinement in its contour;

Figure 5 is a fragmentary schematic View exaggerating the relationship between the desired cam configuration and cutting element to more fully depict the principles of the invention; and

Figure 6 is a fragmentary schematic view exaggerating the relationship between a preferred form of gearing. which strangely enough closely approximates a desired corrective phase shifting movement in the above apparatus.

There is shown in the drawings apparatus embodying principles of the present invention, which is specifically designed to machine. the cam configuration illustrated in Figures 3 and 4 of the drawings. ber C shown in these views is specifically designed for use in. sliding vane cam pumps of the type described-in the Burt, Sung and Farron application Serial No. 623,144,.

filed November 19, 1956 In this type of pump, a cylindrical rotor member (not shown) is mounted within the central opening 10 of the cam, in sliding sealing engagement with the radially innermost projecting parts or lobes 12 of the cam. The rotor carries a plurality ofvanes which are biased radially outwardly into engagement with the camsurface 14, to sweep liquid out of the ,speeds ranging from 1000 to 4000 r.p.m. and at pressures in excess of 1000 p.s.i-. Numerous problems are involved in designing pumps for these conditions. One of these problems is. presented. by leakage from a high pressure valley to a low pressure valley through the clearance between the separating lobe and rotor; and another of these problems is presented by the dynamic forces of the vaneswhich tend to separate them from the cam surface. The

specific cam contour used in the cam member C is a sinusoidal one conforming to the equation r=r +e cos 110.. For a more detailed description of this contour and of the problems of designing pulse free pumps, referencemay be had to the above referred to application.

In his work with such pumps, applicant has found that a great reduction in leakage between the cam surface and. rotor can be accomplished by means of'acylindrical con= tour in the tip of each lobe without harmfully affecting the pulse free operation of the pump. These cylindrical contours should be confined to the tips of the lobes; and should preferably extend over an arc of from about 2 to about 5 degrees.

The method and apparatus used by applicant to ma- The cam body mem-,

chine the cam contour previously described may best be understood by reference to Figure 5 of the drawings, wherein the pertinent angles and distances are shown exaggerated to better illustrate the relationship involved. The desired finished machined contour is generally indicated at 15 and the periphery of a rotatable cutter of predetermined diameter for machining the contour is indicated at 16. There is also shown at 18 a line all points on which are spaced radially inwardly from the line 15 towards the center of the blank a distance R which corresponds to the radius of the cutter 16. Relatively simple means could be provided for moving the center of the rotatable cutter along line 13; but were this to be done, the cutter would not be tangent to the desired contour as seen by the dot-dash line 20, but would dig out too much metal at some spots and not enough at others. In order for the above described cam contour to be able to develop substantially pulse free discharge, the cam contour must be machined to an accuracy approaching a few ten thousandths of an inch. This can only be obtained by correcting for the above-stated inaccuracy involved in the use of a rotatable cutter.

The applicant has theorized that the above errors could be eliminated were means to be provided which, if kept in phase relationship with the angle of rotation of the blank, would move the center of the cutter along a path which is a fixed radial distance from the desired cam contour (i.e. along the line 18); and further has theorized that by suitably changing the phase relationship between the cutter and the blank, the periphery of the cutter could be made tangent to the desired contour at all times. A preferred method of accomplishing these results will now be explained with reference to Figure of the drawings. Assume for the time being that a suitable means is used to provide radial movement between the cutter and the blank, and that a further means is provided which, when rotated in direct proportion to said first means, moves the center of the cutter along the line 18. Referring to Figure 5, the equation for the desired cam contour will be:

r =radius of any point of the cam defined by angle 5 r =mean base circle for the cam =maximum variation above and below the base circle ri=number of lobes =the angle between any particular radius and an arbitrary reference line through a center of a valley.

For a cutter of radius R, the radius of curve 18 at any given point would be r =r R+e cos 11.

It will be seen that if the cutter is moved in and out on its radius in phase with its position about the cam its center would be at 22 at the angle 5 shown in Figure 5. If the center 22 were moved, radially inwardly to the point 24, the cutter would be tangent to the desired contour at the point T. Point 24 is the distance S from the center 0; and if the cutter were moved out of phase by the angle 0, it would have a radius equal to S. Therefore to be tangent, the means moving the cutter radially would have to have moved an angle proportional to B when the cutter had moved By means of polar coordinates:

rewriting 3:

and I 0=% arc cos lfR-rT -l- 81- 5 5 also from the law of sines sin (90 U) sin (OC) 10 Foam sin @gi Constructing a normal from point 24 to the radian a.

. a $111 (90 U) a R sin (90 u cos (90 U) h=r -R cos (90 U) Rsin so-w (5) f (b) T -R cos (90 U) 0:; are cos [R-r +S]a R sin (90 U (i R cos 90- w) where:

- S=Vr R -2r R cos (90 U) and U=arc tan 9 e n sin [20:

The above equation expresses the manner in which 0 must vary with respect to 5 and shows the relationshi between 0 and to'be quite complicated.

Applicant further investigated the manner in which a first cylindrical gear journalled about a point spaced a distance a from its center would rotate a similar gear also journalled a distance a from its center. The arrangement investigated is seen in Figure 6 where the various angles and distances are appropriately labeled and from which the following equations are developed: (7 D =R a 2a R cos (180-P) D =VR +a +2aR cos P R =F +a 2aF cos (180-00) 5 F +2aF cos x-l- (a R) =0 2 2 R2 F: 20, cos win/(2a 2cos x) 4(a (8) F=a cos x;!; /R a sin x F sin z F cos a:+a P=arc sin -)-arc cos (F sin :0) d: are sin D 7 Sin (-a cos :vjn R a sin as) sin a:

45- /R +a +2aR cos P a cos xjn/R a sin x) sina: Qatar: Sm F cos x-l-a 2 2 R fl-a +2aR R (a cos xix R -a sin sin :10

and xshould approach n times the theoretical 0 of Equation 6.

By cut and try methods applicant was able to establish that, when r =1.25, R=.375, n=6, e=.023, R=1 for VR2+3a +2a cos a; (-a cos 14am) the gear, and the a value of the gears =0.106, the gen- 10 erated contour very closely approximates the theoretically desired contour.

A tabulation of data indicating the accuracy with which the S value provided by the gearing approaches the theoretically required S value for a perfect contour is as follows:

Assuming values of a as indicated,

in turn is supported from the slide structure F about to be. described. The top plate 48 of the frame is machined parallel to the machine surface 32 to provide a suitable surface on which the slide structure F reciprocates. Opposite side edges of the slide F are beveled for sliding engagement with a pair of ways 50 and 52 which in turn are bolted to the top plate 48 in a manner assuring that the cutter D will move radially across the centerline of the turntable B. The electric motor E is supported from the slide F by means of blocks 54 and 56, the adjacent ends of which are suitably recessed to receive opposite s' sin a: s sin so-r17 g arc sin g 68 input angle of gears 1: output angle of cos 1 t=0.023 cos I S- (125-375) t-s gears where t=throw of eccentric G.

It will be seen that the maximum error is less than 2 ten thousandths of an inch and is therefore acceptable.

Apparatus embodying the above principles is shown in Figures 1 and 2 of the drawings. The apparatus generally comprises a frame A on which is journalled a turntable B for supporting and rotating an annular blank C to be machined. The blank is machined by a rotatable cutter D carried by a high speed electric motor E, which in turn is mounted on a slide F adapted to be reciprocated so that the cutter moves in a straight line which passes through the center of the blank. The slide F is moved back and forth by means of the eccentric G which in turn is rotated by means of gearing H which provides the proper lead and lag to the in and out movement of the slide to maintain the cutter tangent to the desired contour, as discussed above.

The turntable B for supporting and rotating the blank C comprises a bottom plate 30, the under surface of which is accurately machined to revolve on a corresponding surface 32 machined into the top face of a horizontal plate 34 of the frame A. A facing plate 36 recessed in its upper face to receive the bottom end of the cutter D and to provide chip space is suitably fastened to the plate 30; and the blank C is adapted to be clamped thereto by the bolts 38. The turntable assembly 13 is rotated by means of a shaft 40 suitably journalled in the frame A; and the bottom end of shaft 40 is coupled to the output shaft 42 of a gear reducer 44 having an input shaft 46 adapted to be driven by an electric motor (not shown).

The blank C will usually be rough machined to an internal diameter approaching the desired distance between opposite lobes of the finished cam. The rotatable cutting element D adapted to machine the finished contour is rotatably supported from the electric motor E which sides of the electric motor E; and the electric motor is clamped therebetween by means of the machine bolts 62. The block 54 is in turn adjustably positioned upon the slide F by means of a plurality of bolts 64 which extend through slotted holes 66 in the block 54 and are threaded into the slide plate F. Suitable openings 68 and 70 are provided in the slide plate F and the top plate 48 of the frame, respectively, to receive the electric motor E and permit lateral movement thereof relative to the blank C.

The slide F is adapted to be reciprocated generally according to a desired sinusoidal function by an eccentric G and a Scotch yoke structure 72 fixed to the slide plate F. The Scotch yoke structure 72' is formed by means of a pair of blocks 74 and 76 adjacent sides of which are suitably recessed to receive opposite sides of a cylindrical rotor 78. The blocks 74 and 76 are confined into tight engagement with opposite sides of the rotor 78 by means of a crossbar 80 and through bolts 82 and 84 which extend through openings in opposite side spacer members 86 and 88 and are threaded into the end of the slide plate F. The spacer members 86 and 88 are of a length which will provide a tight fit between the rotor 78 and the blocks 74 and 76 to overcome lost motion in the reciprocating structure. The reciprocating cycle of the cutter D may be fed radially outwardly into the blank by means of a hand Wheel 90 and rod 92 which is threaded into a support block 94 and the end of which is adapted to abut the block 54. The support block 94 is fixed to slide F by bolts 96; and the end of the rod 92 adjacent the hand Wheel 90 is slidably received in an opening 98 in a guide plate 100 suitably fixed to the frame A. The block 54 carrying the motor E has been previously described as being adjustably fixed tothe slide plate F by means of slotted holes 66 and bolts 64; and by threading the rod 92 inwardly against the block 54, the block 54 may be moved relative to the slide plate F. A dial indicator 102 is shown mounted on the block 54 with its sensitive element in engagement with the support block 94 so that the depth of cut of the cutter D can be readily determined. As a practical matter, the bolts 64 may be tightened to a point wherein friction between the block 54 and slide plate F is sufficient to hold the cutter into cutting engagement with the blank and yet still permit the block 54 to be moved relative to the slide by means of the threaded rod 92 without further adjustment of the bolts 64.

The cylindrical rotor 78 is mounted eccentrically on the end of a shaft 104 by a distance e which in the present instance is equal to 0.023 inch. The shaft 104 is suitably journaled in the frame A and is driven at a rate which is generally six times that at which the blank is rotated to provide a cam having six lobes and six valleys. The shaft 104 is driven from a jackshaft 106 by means of gearing H later to be described, and the jackshaft 186 is suitably journalled in the frame A and driven at a rate six times that of the shaft 40 by means of gears 108 and 110 fixed to the shafts 4t) and 166 respectively.

The gear means H is adapted to provide the correction by means of which the cutter element D is maintained tangent to the desired cam contour, utilizing the principles previously described with reference to Figure 6 of the drawing. The gear means H comprises two cylindrical gears each having a pitch diameter of two inches and each of which is mounted on its respective shaft eccentrically by a distance a, which in the present instance is equal to 0.106 inch. The gear 112 which is fixed to the shaft 106 will correspond generally to the left-hand gear depicted in Figure 6; and the gear 114 fixed to the shaft 104 will correspond to that shown in the right-hand side of the same figure.

In the preferred method of operating the apparatus above described, a gear blank C finished to a rough internal diameter will be bolted to the turntable B. The cutter D will be positioned within the opening of the blank C, and the gear 112 will be removed from the shaft 104 so that the slide P will not be reciprocated relative to the blank. The hand wheel 90 will be turned to gradually advance the rotating cutter D radially into the blank C until its internal diameter corresponds to the desired distance between the cylindrical surfaces 116 in opposite lobes of the finished cam. Once this diameter has been accurately machined, the gear 112 is inserted upon the shaft 106 and the eccentric means G suitably rotated to provide reciprocatory movement of slide structure F. Prior to the time that the slide structure F is reciprocated relative to the blank, the motor B will be moved radially inwardly a sufiicient distance such that the cutter D will not engage the surfaces of the blank about to be machined when the reciprocation of the slide structure is started. Thereafter the rod 92 is threaded inwardly until the reciprocatory cycle is moved outwardly to a point where the cutter D begins to engage the blank during the radially outermost portion of its cycle. Engagement of the cutter D during its outermost extremity of radial movement begins to form the valleys in the blank C; and by gradually advancing the rod 92 into the support member 94, these valleys will be deepened until all that remains of the orginal cylindrical internal surface are the sections which are to be left in the tips of each of the lobes. These cylindrical surfaces 116 will preferably be from 2 to degrees in length. It will be seen that the chordal length of the cylindrical surfaces 116 will be gradually reduced as the machining of the cam progrmses. The cylindrical surfaces 116 provide a mark which can readily be seen by the operator; and when this mark has decreased to approximately 50 or 60 thousandths of an inch (which can be judged by eye by a skilled machinist) the machining of the cam is complete. By this simple expedient the sinusoidal surfaces can be accurately machined to the desired depth. The apparatus shown in the drawings can be used to machine external cams as well as internal cams; and by suitably altering the eccentric Gy and gearing H, the same principles can be used to form cams having a configuration other than the sinusoidal one of the cam shown in Figure 3.

While the invention has been described in considerable detail, I do not wish to be limited to the particular methabout a predetermined axis; a slide for supporting a rotatable cutting element on an axis parallel to said first mentioned axis, said slide being movable in a radial direction with respect to said first mentioned axis; a first shaft having an eccentric thereon; means abutting opposite sides of said eccentric for reciprocating said slide; a second shaft; a pair of generally cylindrically shaped gears in driving engagement, one of said gears being fixed to said first shaft on an axis located to one side of its geometric center, and the other of said gears being fixed to said second shaft on an axis located to one side of its geometric center; a third shaft for rotatably driving said blank supporting means; and a second set of gears operatively connected between said second and third shafts for rotating said shafts in predetermined relationship.

2. Apparatus constructed substantially in accordance with claim 1 and wherein: the distance between the geometrical center and the axis of rotation for each of said first mentioned pair of generally cylindrically shaped gears is substantially identical.

3. Cam cutting apparatus for forming sinusoidal cams comprising: a cutting tool rotatable about a predetermined axis, said tool having peripheral side cutting edges which are generally parallel to said axis; a work table for supporting a work blank in a manner to be machined by said peripheral edges of said cutting tool; first drive mechanism for producing relative motion between said cutting tool and said work table in a first direction which causes the work blank mounted on said work table and the peripheral edge of said cutting tool to move generally tangentially relative to the peripheral edge of said cutting tool, the motion of said work table being directly proportional to input motion to said first drive mechanism; second drive mechanism for producing relative motion between said cutting tool and said blank in a direction generally normal to said axis of said cutting tool and generally normal to said first tangential direction, said relative motion in said normal direction being a sinusoidal function of input motion to said second drive mechanism; power means driving one of said first and second drive mechanisms; and a pair of engaging cylindrical gears each of which are rotated about respective shafts each of which are located a predetermined distance from the geometric centers of their respective gears, one of said shafts being rotated by said power means and the other of said shafts operatively driving the other of said first and second drive mechanisms.

4. Cam cutting apparatus for forming sinusoidal cams comprising: a cutting tool rotatable about a predetermined axis, said tool having peripheral side cutting edges which are generally parallel to said axis; a work table for supporting a work blank in a manner to be machined by said peripheral edges of said cutting tool; first drive mechanism for producing relative motion between said cutting tool and said work table in a first direction which causes the work blank mounted on said work table and the peripheral edge of said cutting tool to move generally tangentially relative to the peripheral edge of said cutting tool, the motion of said work table being directly proportional to input motion to said first drive mechanism; second drive mechanism for moving said cutting tool in a direction generally normal to said axis of said cutting tool and generally normal to said first tangential direction, said motion in said normal direction being a sinusoidal function of input motion to said second drive mechanism; power means driving one of said first and second drive mechanisms; and a pair of engaging cylindrical gears each of which are rotated about respective shafts each of which are located a predetermined distance from the geometric centers 01". their respective gears, one of said shafts being rotated by said power means and the other of said shafts operatively driving the other of said first and second drive mechanisms.

5. Cam cutting apparatus for forming sinusoidal cams comprising: a cutting tool rotatable about a predetermined axis, said tool having peripheral side cutting edges which are generally parallel to said axis; a work table for supporting a work blank in a manner to be machined by said peripheral edges of said cutting tool; first drive mechanism for moving said work table in a first direction which causes the work blank mounted on said Work table to move generally tangentially relative to the peripheral edge of said cutting tool, the motion of said work table being directly proportional to input motion to said first drive mechanism; second drive mechanism for moving said cutting tool in a direction generally normal to said axis of said cutting tool and generally normal to said first tangential direction, said motion in said normal direction being a sinusoidal function of input motion to said second drive mechanism; power means driving one of said first and second drive mechanisms; and a pair of engaging cylindrical gears each of which are rotated about respective shafts each of which are located a predetermined distance from the geometric centers of their respective gears, one of said shafts being rotated by said power means and the other of said shafts operatively driving the other of said first and second drive mechanisms.

6. Cam cutting apparatus for forming sinusoidal cams comprising: a cutting tool rotatable about a predetermined axis, said tool having peripheral side cutting edges which are generally parallel to said axis; a work table for supporting a work blank in a manner to be machined by said peripheral edges of said cutting tool; first drive mechanism for rotating said work table in a first direction which causes the work blank mounted on said work table to move generally tangentially relative to the peripheral edge of said cutting tool, the rotation of said work table being directly proportional to input motion to said first drive mechanism; second drive mechanism for moving said cutting tool in a direction generally normal to said axis of said cutting tool and generally normal to said first tangential direction, said motion in said normal direction being a sinusoidal function of input motion to said second drive mechanism; power means driving one of said first and second drive mechanisms; and a pair of engaging cylindrical gears each of which are rotated about respective shafts each of which are located a predetermined distance from the geometric centers of their respective gears, one of said shafts being rotated by said power means and the other of said shafts operatively driving the other of said first and second drive mechanisms.

References Cited in the file of this patent UNITED STATES PATENTS 1,307,202 Kenney June 17, 1919 2,507,800 Mekelburg May 16, 1950 2,517,142 Staley Aug. 1, 1950 2,616,337 Tappert et al Nov. 4, 1952 2,633,776 Schenk Apr. 7, 1953 2,660,930 De Vlieg et al. Dec. 1, 1953 2,675,742 Petre Apr. 20, 1954 2,714,336 Schmidt Aug. 2, 1955 2,734,428 Onsrud Feb. 14, 1956 2,753,765 Touchman July 10, 1956 UNITED STATES PATENT OFFICE CERTIFICATION OF CORRECTION Patent No. 2,958,264 November 1, 1960 Farlow B.. Burt ppears in the above numbered pat- It is hereby certified that error e id Letters Patent should read as ent requiring correction and that the sa. corrected below.

lines 64 and 65 for that portion of the Column 4, equation reading F cos x+a" read F cos x+a Signed and sealed this 6th day of June 1961.

(SEAL) Attest:

ERNEST W. SWIDER Attesting Officer DAVID L. LADD Commissioner of Patents 

